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Implicit Function with Natural Behavior over Entire Domain

Taku ITOH, Ayumu SAITOH¹⁾, Atsushi KAMITANI²⁾ and Hiroaki NAKAMURA³⁾

Seikei University, 3-3-1 Kichijoji-Kitamachi, Musashino, Tokyo 180-8633, Japan

1)

University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan

2)

Yamagata University, 4-3-16 Johnan, Yonezawa, Yamagata 992-8510, Japan

3)

National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan

(Received 10 December 2011 / Accepted 7 March 2012 / Published 13 September 2012)

Abstract

To generate a smooth implicit function that behaves naturally over an entire domain, a method to smoothly combine an implicit function f(x) with a global support function g(x) has been proposed. The proposed method can be applied to large scattered point data, since the implicit function f(x) is generated by a partition-of-unity-based method. The global support function g(x) is generated by a radial basis function-based method or by the least-squares method. To ensure a smooth combination of f(x) and g(x), an appropriate weight function is employed. In numerical experiments, the proposed method is applied to large point data. The results illustrate that the proposed method can generate a smooth implicit function F(x) with natural behavior over the entire domain. In addition, on the given points, the accuracy of F(x) is exactly the same as that of f(x). Furthermore, the computational cost for generation of F(x) is almost the same as that of f(x).

Copyright (c) 2012 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

implicit function, meshless method, extended boundary-node method, partition of unity, radial basis function, smooth combination

DOI: 10.1585/pfr.7.2406068

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References

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This paper may be cited as follows:

Taku ITOH, Ayumu SAITOH, Atsushi KAMITANI and Hiroaki NAKAMURA, Plasma Fusion Res. 7, 2406068 (2012).